scholarly journals Establishing non-Abelian topological order in Gutzwiller-projected Chern insulators via entanglement entropy and modularS-matrix

2013 ◽  
Vol 87 (16) ◽  
Author(s):  
Yi Zhang ◽  
Ashvin Vishwanath
Keyword(s):  
Entanglement Entropy ◽  
Topological Order ◽  
Chern Insulators

scholarly journals Observation of fractional Chern insulators in a van der Waals heterostructure

Science ◽  
2018 ◽  
Vol 360 (6384) ◽  
pp. 62-66 ◽  
Author(s):  
Eric M. Spanton ◽  
Alexander A. Zibrov ◽  
Haoxin Zhou ◽  
Takashi Taniguchi ◽  
Kenji Watanabe ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Boron Nitride ◽  
Symmetry Breaking ◽  
Hexagonal Boron Nitride ◽  
Landau Levels ◽  
Topological Order ◽  
Hall Conductance ◽  
Van Der Waals Heterostructure ◽  
Ordered Phases ◽  
Chern Insulators

Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional fillings of topologically nontrivial Chern bands. Here we report the observation of gapped states at fractional fillings of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene–hexagonal boron nitride heterostructure. We observed phases at fractional filling of bands with Chern indices C=−1, ±2, and ±3. Some of these phases, in C=−1 and C=2 bands, are characterized by fractional Hall conductance—that is, they are known as fractional Chern insulators and constitute an example of topological order beyond Landau levels.

scholarly journals Detecting subsystem symmetry protected topological order via entanglement entropy

2019 ◽  
Vol 100 (11) ◽  
Author(s):  
David T. Stephen ◽  
Henrik Dreyer ◽  
Mohsin Iqbal ◽  
Norbert Schuch
Keyword(s):  
Entanglement Entropy ◽  
Topological Order ◽  
Symmetry Protected

scholarly journals Entanglement entropy for (3+1)-dimensional topological order with excitations

2018 ◽  
Vol 97 (8) ◽  
Author(s):  
Xueda Wen ◽  
Huan He ◽  
Apoorv Tiwari ◽  
Yunqin Zheng ◽  
Peng Ye
Keyword(s):  
Entanglement Entropy ◽  
Topological Order

scholarly journals Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons

2017 ◽  
Vol 29 (06) ◽  
pp. 1750018 ◽  
Author(s):  
Sven Bachmann
Keyword(s):  
Ground State ◽  
Entanglement Entropy ◽  
Orientable Surface ◽  
Cell Complex ◽  
Local Order ◽  
Topological Order ◽  
Cohomology Groups ◽  
Closed Orientable Surface ◽  
Ground State Degeneracy ◽  
Comprehensive Study

In this comprehensive study of Kitaev’s abelian models defined on a graph embedded on a closed orientable surface, we provide complete proofs of the topological ground state degeneracy, the absence of local order parameters, compute the entanglement entropy exactly and characterize the elementary anyonic excitations. The homology and cohomology groups of the cell complex play a central role and allow for a rigorous understanding of the relations between the above characterizations of topological order.

scholarly journals Universal entanglement signatures of foliated fracton phases

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Wilbur Shirley ◽  
Kevin Slagle ◽  
Xie Chen
Keyword(s):  
Fixed Point ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Topological Phases ◽  
Topological Order ◽  
Two Dimensional ◽  
Adiabatic Evolution ◽  
Universal Properties ◽  
Three Dimensional Models ◽  
Topological Entanglement Entropy

Fracton models exhibit a variety of exotic properties and lie beyond the conventional framework of gapped topological order. In , we generalized the notion of gapped phase to one of foliated fracton phase by allowing the addition of layers of gapped two-dimensional resources in the adiabatic evolution between gapped three-dimensional models. Moreover, we showed that the X-cube model is a fixed point of one such phase. In this paper, according to this definition, we look for universal properties of such phases which remain invariant throughout the entire phase. We propose multi-partite entanglement quantities, generalizing the proposal of topological entanglement entropy designed for conventional topological phases. We present arguments for the universality of these quantities and show that they attain non-zero constant value in non-trivial foliated fracton phases.

scholarly journals Identifying topological order by entanglement entropy

2012 ◽  
Vol 8 (12) ◽  
pp. 902-905 ◽  
Author(s):  
Hong-Chen Jiang ◽  
Zhenghan Wang ◽  
Leon Balents
Keyword(s):  
Entanglement Entropy ◽  
Topological Order
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